Several condensations heated externally by nearby hot stars are present in the Sgr B2 region for which H2O far-IR lines are expected to probe only an external low-density and high temperature section. Millimeter-wave lines can penetrate deeper into them (higher densities and lower Tk). We have conducted a study combining H2O lines in both spectral regions using the ISO (far-IR lines) and the IRAM 30 m telescope (183 GHz line). The far-IR H2O lines, seen in absorption, are optically thick. They form in the outermost gas in front of the far-IR continuum sources, probing a maximum visual extinction of ~5-10 mag. IR photons from the dust play a dominant role in their excitation. We conclude, based on observations of the CO J=7-6 line at 806.65 GHz, and the lack of emission from the far-IR CO lines, that the gas density has to be below ~104 cm-3. Using the gas kinetic temperature and density derived from OH, CO, and other molecular species, we derive a water column density of (9+/-3)×1016 cm-2 in the absorbing gas, implying an abundance of ~=(1-2)×10-5 in this region. The resulting relatively low H2O/OH abundance ratio, ~=2-4, is a signature of UV photon-dominated surface layers traced by far-IR observations. As a consequence, the temperature of the absorbing gas is high, Tk~=300-500 K, which allows very efficient neutral-neutral reactions producing H2O and OH. Finally, the 183.31 GHz data allow one to trace the inner, denser (n(H2)>=105-106 cm-3), and colder (Tk~40 K) gas. The emission is very strong toward the cores with an estimated water vapor abundance of a few × 10-7. There is also moderate extended emission around Sgr B2 main condensations, in agreement with the water vapor abundance derived from far-IR H2O lines. Based on observations with ISO, an ESA project with instruments funded by ESA Member States (especially the PI countries: France, Germany, the Netherlands, and the United Kingdom) and with participation of ISAS and NASA.